Two parallel amps may be fine, but unless you're using matched resistors or very tight tolerance ones, their gains will be slightly different basically always, so keeping it single ended then converting to differential minimizes the independent drift/variation of two channels somewhat.
If it were me, I'd lay it out differently, there seems to be a fair bit of extra parts in this design. First stage would be a unity gain inverting amp (like the output stages right now) but with the potentiometer in series with the feedback resistor, then a small capacitor in parallel with the pair of feedback resistors to take out high frequency noise above the audio band. That would give you plenty of gain, and depending on the input impedance of your target device, you could either have a single inverting unity gain amp to give you the inverse signal and just the output of the gain stage to drive the negative differential output directly (half the number of opamps, many fewer parts), or, if you need to be able to source some current, you could have an inverting unity gain amp and a follower amp after the gain stage (3 opamps, but now each differential output stage can drive the full current rated for the opamp). If running a single supply instead of a split supply, then you'd also want a cap on the output to remove the DC bias, and the resistor on the output probably doesn't need to be so high unless you want full protection from a constant short on the output.